Toss tomatoes, olives, capers, and 2 tablespoons oil together in a medium bowl. Set aside. Season both sides of chicken with salt and pepper.
Heat remaining tablespoon oil in a large ovenproof skillet over medium- high heat until hot but not smoking.
Brown chicken in skillet in a single layer (in batches if necesssary); cook until deep golden brown, on one side, about 4 minutes. Remove to a plate and continue browning remaining chicken.
Return all chicken to skillet, uncooked-side down. Add tomato mixture to skillet, gently shaking skillet to distribute.
Cover and cook until chicken is cooked through and tomatoes have softened, about 10 minutes.
This festive chicken dish is delicious paired with quinoa or rustic bread and a big Greek salad.